Project 2: Breast Cancer Predictions

by: Devansh Bhavsar, Guadalupe Higuera, Munachimso Aneke

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import MinMaxScaler
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import confusion_matrix, accuracy_score
import scipy.stats as sci
import plotly.express as px
pd.options.mode.chained_assignment = None

Motivation and background. (About data and Problem)

The motivation for this project is that breast cancer is the second leading cause of death of women in America according to cancer.gov. Breast cancer can be either benign or malignant. For a benign cancer, a woman may be able to live a healthy life without needing to worry about the cancer, however a malignant cancer may be something that must be taken with urgency.

• However, according to cancer.gov, screening test can have harms such as the harms of a mammograph. False-positive test results can occur.
• False-positive results can lead to extra testing and cause anxiety.
• False-negative test results can delay diagnosis and treatment.
• Finding breast cancer may lead to breast cancer treatment and side effects, but it may not improve a woman's health or help her live longer.
• Mammography exposes the breast to low doses of radiation.
• There may be pain or discomfort during a mammogram. If we can differentiate a cancer from benign or malignant, a tool can be developed that can allow for doctors to determine if screenings are to be needed.

For that reason, we choose a breast cancer dataset provided from Kaggle.

breast_cancer_df = pd.read_csv('data.csv')
breast_cancer_df.head(5)

	id	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	...	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst	Unnamed: 32
0	842302	M	17.99	10.38	122.80	1001.0	0.11840	0.27760	0.3001	0.14710	...	17.33	184.60	2019.0	0.1622	0.6656	0.7119	0.2654	0.4601	0.11890	NaN
1	842517	M	20.57	17.77	132.90	1326.0	0.08474	0.07864	0.0869	0.07017	...	23.41	158.80	1956.0	0.1238	0.1866	0.2416	0.1860	0.2750	0.08902	NaN
2	84300903	M	19.69	21.25	130.00	1203.0	0.10960	0.15990	0.1974	0.12790	...	25.53	152.50	1709.0	0.1444	0.4245	0.4504	0.2430	0.3613	0.08758	NaN
3	84348301	M	11.42	20.38	77.58	386.1	0.14250	0.28390	0.2414	0.10520	...	26.50	98.87	567.7	0.2098	0.8663	0.6869	0.2575	0.6638	0.17300	NaN
4	84358402	M	20.29	14.34	135.10	1297.0	0.10030	0.13280	0.1980	0.10430	...	16.67	152.20	1575.0	0.1374	0.2050	0.4000	0.1625	0.2364	0.07678	NaN

5 rows × 33 columns

Data Cleaning

For cleaning, the column labeled "Unamed: 32" is removed because it is filled with missing values. The "id" column is also deleted as the id's are not needed for the analysis.

breast_cancer_df = breast_cancer_df.drop(labels="id", axis=1)
breast_cancer_df = breast_cancer_df.drop(labels="Unnamed: 32", axis=1)
breast_cancer_df = breast_cancer_df.dropna(axis=1)
breast_cancer_df.head(5)

	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	...	radius_worst	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst
0	M	17.99	10.38	122.80	1001.0	0.11840	0.27760	0.3001	0.14710	0.2419	...	25.38	17.33	184.60	2019.0	0.1622	0.6656	0.7119	0.2654	0.4601	0.11890
1	M	20.57	17.77	132.90	1326.0	0.08474	0.07864	0.0869	0.07017	0.1812	...	24.99	23.41	158.80	1956.0	0.1238	0.1866	0.2416	0.1860	0.2750	0.08902
2	M	19.69	21.25	130.00	1203.0	0.10960	0.15990	0.1974	0.12790	0.2069	...	23.57	25.53	152.50	1709.0	0.1444	0.4245	0.4504	0.2430	0.3613	0.08758
3	M	11.42	20.38	77.58	386.1	0.14250	0.28390	0.2414	0.10520	0.2597	...	14.91	26.50	98.87	567.7	0.2098	0.8663	0.6869	0.2575	0.6638	0.17300
4	M	20.29	14.34	135.10	1297.0	0.10030	0.13280	0.1980	0.10430	0.1809	...	22.54	16.67	152.20	1575.0	0.1374	0.2050	0.4000	0.1625	0.2364	0.07678

5 rows × 31 columns

Data Summary

A quick summary of the numeric variables in the dataset

summary = breast_cancer_df.describe().loc[['mean', '50%', 'std', 'min', 'max'], :]
summary.rename(index={'mean':'Mean','50%': 'Median', 'std': 'Standard Deviation', 'min':'Min', 'max':'Max'}, inplace=True)
summary

	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	fractal_dimension_mean	...	radius_worst	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst
Mean	14.127292	19.289649	91.969033	654.889104	0.096360	0.104341	0.088799	0.048919	0.181162	0.062798	...	16.269190	25.677223	107.261213	880.583128	0.132369	0.254265	0.272188	0.114606	0.290076	0.083946
Median	13.370000	18.840000	86.240000	551.100000	0.095870	0.092630	0.061540	0.033500	0.179200	0.061540	...	14.970000	25.410000	97.660000	686.500000	0.131300	0.211900	0.226700	0.099930	0.282200	0.080040
Standard Deviation	3.524049	4.301036	24.298981	351.914129	0.014064	0.052813	0.079720	0.038803	0.027414	0.007060	...	4.833242	6.146258	33.602542	569.356993	0.022832	0.157336	0.208624	0.065732	0.061867	0.018061
Min	6.981000	9.710000	43.790000	143.500000	0.052630	0.019380	0.000000	0.000000	0.106000	0.049960	...	7.930000	12.020000	50.410000	185.200000	0.071170	0.027290	0.000000	0.000000	0.156500	0.055040
Max	28.110000	39.280000	188.500000	2501.000000	0.163400	0.345400	0.426800	0.201200	0.304000	0.097440	...	36.040000	49.540000	251.200000	4254.000000	0.222600	1.058000	1.252000	0.291000	0.663800	0.207500

5 rows × 30 columns

Univariate Analysis

The bar plot below shows that the dataset has more cases with beningn (B) tumour than malignant (m) tumours.

target_plot = sns.countplot(data=breast_cancer_df, x='diagnosis', hue='diagnosis')
target_plot.set(title="Barplot of Diagnosis" )
target_plot.bar_label(target_plot.containers[0])
target_plot.bar_label(target_plot.containers[1])
plt.show()

Scatter plots with Linear Regression

We wanted to see the relationship between different factors of a tumor and how they affect the severity of cancer so being benign or malignant. We made 3 scatter plots with linear regression.

Plot 1: Average Area vs Average Radius of Tumor

graph = sns.relplot(data=breast_cancer_df, x="radius_mean",y="area_mean", hue="diagnosis").set(title="How Average size of Tumor affects Serverity of Cancer")
graph.map(sns.regplot, "radius_mean","area_mean",ci=0, scatter=False, color='black')
graph.set_xlabels("Average Radius")
graph.set_ylabels("Average Area")

<seaborn.axisgrid.FacetGrid at 0x7fea98d52e80>

Analysis

The first plot shows the relationship ship between average radius and average area. It can clearly be deduced that the more the radius and the more the area of a tumor is the higher the chances of the tumor being malignant. This graph also pointed out that radius and area go hand in hand so in the later graphs we will mostly only refer to area as it will take radius into account anyways.

Plot 2: Average Compactness vs Average Concavity of Tumor

graph1 = sns.relplot(data=breast_cancer_df, x="compactness_mean",y="concavity_mean", hue="diagnosis").set(title="How Average Concavity and Compactness of Tumor affects severity of Cancer")
graph1.map(sns.regplot, "compactness_mean","concavity_mean",ci=0, scatter=False, color='black')
graph1.set_xlabels("Average Compactness")
graph1.set_ylabels("Average Concavity")

<seaborn.axisgrid.FacetGrid at 0x7fea9947e048>

Analysis

The second plot shows the relationship between average concavity and average compactness. We felt like these two factors described the overalll shape and hardness of the tumor and accoriding to the linear regression, the more the compact and concave the tumor is the more changes of it being malignant.

Plot 3: Average Smoothness vs Average Texture of Tumor

graph2 = sns.relplot(data=breast_cancer_df, x="smoothness_mean",y="texture_mean", hue="diagnosis").set(title="How Average Texure and Smoothness of Tumor affects severity of Cancer")
graph2.map(sns.regplot, "smoothness_mean","texture_mean",ci=0, scatter=False, color='black')
graph2.set_xlabels("Average Smoothness")
graph2.set_ylabels("Average Texture")

<seaborn.axisgrid.FacetGrid at 0x7fea99ceeda0>

Analysis

This third plot shows the relationship between average texture and average smoothness of a tumor. Basing our analysis off of the scatter plot and linear regression line there is an obvious relationship between these two factors.

M_data = breast_cancer_df.loc[breast_cancer_df["diagnosis"]=="M"]
B_data = breast_cancer_df.loc[breast_cancer_df["diagnosis"]=="B"]

colors = ["green","purple"]
fig, axs = plt.subplots(1,3)
fig.suptitle("Analysis of Average Area, Compactness, and Concavity")
b1 = axs[0].boxplot([B_data["area_mean"],M_data["area_mean"]], patch_artist=True, labels=["Benign","Malignant"])
axs[0].set_xlabel("Average Area")
for patch, color in zip(b1['boxes'], colors):
    patch.set_facecolor(color)


b2 = axs[1].boxplot([B_data["compactness_mean"],M_data["compactness_mean"]], patch_artist=True, labels=["Benign","Malignant"])
axs[1].set_xlabel("Average Compactness")
for patch, color in zip(b2['boxes'], colors):
    patch.set_facecolor(color)

b3 = axs[2].boxplot([B_data["concavity_mean"],M_data["concavity_mean"]], patch_artist=True, labels=["Benign","Malignant"])
axs[2].set_xlabel("Average Concavity")
for patch, color in zip(b3['boxes'], colors):
    patch.set_facecolor(color)

fig.legend([b1["boxes"][0], b1["boxes"][1]],["Bengin","Malignant"],bbox_to_anchor=(1.04,1), loc="upper left")
fig.tight_layout()
plt.show

<function matplotlib.pyplot.show(close=None, block=None)>

Analysis

We created a side-by-side boxplot comparing the average area, average compactness, and average concavity of the tumor separated by whether the tumor was diagnosed as bengin or malignant. We were able to confirm that all malignant tumors have a significantly higher average area, average compactness, and average concavity.

3D Plot Analysis of Area, Compactness, and Concavity

This final 3D graph is to visualize the relationship between average area, average compactness, and average concavity. It proves that the higer the area, compactness and concavity of a tumor, the higher the chances of that tumor being malignant.

fig = px.scatter_3d(breast_cancer_df, x='area_mean', y='compactness_mean',z='concavity_mean', color='diagnosis', symbol='diagnosis', size_max=18, opacity=0.8)
fig.update_layout(title = "Average Mean vs Compactness vs Concavity",scene = dict(
   xaxis_title='Average Mean',
   yaxis_title='Average Compactness',
   zaxis_title='Average Concavity'),)
fig.show(renderer='notebook')

Analysis

This final 3D graph is to visualize the relationship between average area, average compactness, and average concavity. It proves that the higer the area, compactness and concavity of a tumor, the higher the chances of that tumor being malignant.

Modeling: K-Nearest Neighbors

To make it easier for the model to learn, we are going to change B to 0 and M to 1 so that way the model is able to differentiate from a benign cancer and malignant

breast_cancer_df_model = breast_cancer_df[["diagnosis","radius_mean", "texture_mean", "area_mean", "compactness_mean", "concavity_mean", "smoothness_mean"]]
for index, row in breast_cancer_df_model.iterrows():
    if row.diagnosis == "B":
        breast_cancer_df_model.loc[index, "diagnosis"] = 0
    else:
        breast_cancer_df_model.loc[index, "diagnosis"] = 1

We are going to split the data into two part, one with the independent variables which include our training points that we feel is best for indicating the type of cancer. The dependent variable, the type of cancer will be separated so we can use it for training and checking for whether or model is accurate

Preprocessing and Splitting Data

To build the model using K-Nearest Neighbors (KNN), the data is first sliced into the independent and dependent variables. Then the data is split into the test and train sets. For this project 75% of the data is used to train the model, while the remaining 25% is used to test the model. Feature scaling (normalization) is applied since KNN is a distance based model.

X = breast_cancer_df_model.iloc[:, 1:].values 
y = breast_cancer_df_model.iloc[:, 0].values  

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=123)

norm = MinMaxScaler()
X_norm_train = norm.fit_transform(X_train)
X_norm_test = norm.fit_transform(X_test)

We choose 75% as training data, 25% is testing data. Since we have 425 samples or so, square root of 425 is about 20.5. We initially choose 20 and 21 and our number of neighbors. After choosing our neighbors, we made our two models.

knn_20 = KNeighborsClassifier(n_neighbors=20)
knn_21 = KNeighborsClassifier(n_neighbors=21)

y_train = y_train.astype('int')

knn_20.fit(X_train, y_train)
knn_21.fit(X_train, y_train)
type(knn_20)

sklearn.neighbors._classification.KNeighborsClassifier

After creating the models, we tested the 2 models using the remaining 25% of data. This data does not show the type of cancer, our model will output a array of either 0 or 1 indicating the type of predicted cancer.

knn_20_predict = knn_20.predict(X_test)
knn_21_predict = knn_21.predict(X_test)

Evaluation of Model

Confusion Matrix & Accuracy

We found that both models have an accuracy of 88%. We made a confusion matrix and plot that indicates whether the cancer was correctly identified along with any mistakes such as false positive and false negative.

y_test = y_test.astype('int')
cmatrix_20 = confusion_matrix(y_test, knn_20_predict)
acscore_20= accuracy_score(y_test, knn_20_predict)

cmatrix_21 = confusion_matrix(y_test, knn_21_predict)
acscore_21= accuracy_score(y_test, knn_21_predict)

print(f"The KNN model where k = 20 has an accuracy rate of {round(acscore_20*100, 2)}%")
print(f"The KNN model where k = 21 has an accuracy rate of {round(acscore_21*100, 2)}%")

fig, ax =plt.subplots(1,2, figsize = (10,5))
sns.heatmap(cmatrix_20, annot=True, cbar=False, cmap=plt.cm.Blues, ax=ax[0])
sns.heatmap(cmatrix_21, annot=True, cbar=False, cmap=plt.cm.Blues, ax=ax[1])
ax[0].set(title = "K-value = 20")
ax[1].set(title = "K-value = 21")
fig.suptitle("Confusion Matrix Plot")
fig.supxlabel('Predicted Label')
fig.supylabel('True Label')
plt.show()

The KNN model where k = 20 has an accuracy rate of 88.81%
The KNN model where k = 21 has an accuracy rate of 88.81%

Error Rate vs K-value

Looking at the accuracy rate and confusion matrix for the models, K-value at 20 and 21 produce the same results- 88.81% accuracy. Ploting the means of error at each Kvalue could be helpful in creating a better model. Since our models we very quick to train and test. We decided to see whether the number of neighbors from 1 to 30 had a better accuracy.

error = []

for i in range(1, 30):
    knn = KNeighborsClassifier(n_neighbors=i)
    knn.fit(X_train, y_train)
    y_pred = knn.predict(X_test)
    error.append(np.mean(y_pred != y_test))

plt.figure(figsize=(10, 5))
plt.plot(range(1, 30), error,  linestyle='dashed', marker='o',
         markerfacecolor='red', markersize=10)
plt.title('Error Rate vs K Value')
plt.xlabel('K Value')
plt.ylabel('Error Rate')
plt.show()

Improving the Model

From the graph above, we can see that there is a lower error rate when K-value is equal to 6.

knn_6 = KNeighborsClassifier(n_neighbors=6)
knn_6.fit(X_train, y_train)
knn_6_predict = knn_6.predict(X_test)
cmatrix_6= confusion_matrix(y_test, knn_6_predict)
acscore_6= accuracy_score(y_test, knn_6_predict)

print(f"The KNN model where k = 6 has an accuracy rate of {round(acscore_6*100, 2)}%")

c_6 = sns.heatmap(cmatrix_6, annot=True, cbar=False, cmap=plt.cm.Blues)
c_6.set_title("Confusion Matrix Plot")
c_6.set_xlabel('Predicted Label')
c_6.set_ylabel('True Label')
plt.show()

The KNN model where k = 6 has an accuracy rate of 89.51%